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We study the equation of state of hyperon-rich matter for neutron stars using an extended relativistic mean-field model. We take special care of the recently proposed non-linear behaviour of the vector field which gives a much better description of Dirac-Brückner calculations. The hyperon-hyperon interaction is also implemented by introducing additional meson exchanges. These new terms avoid the instability found at high densitites in previous works while keeping the excellent description for finite nuclear systems. We also demonstrate within the mean-field approach that the presence of hyperons inside neutron stars on one hand and the hyperon-hyperon interactions on the other hand make the onset of kaon condensation less favourable.

We investigate the chiral phase transition at nonzero temperature T and baryon-chemical potential µ B within the framework of the linear sigma model and the Nambu-Jona-Lasinio model. For small bare quark masses we find in both models a smooth crossover transition for nonzero T and µ B = 0 and a first order transition for T = 0 and nonzero µ B . We calculate explicitly the first order phase transition line and spinodal lines in the (T, µ B ) plane. As expected they all end in a critical point. We find that, in the linear sigma model, the sigma mass goes to zero at the critical point. This is in contrast to the NJL model, where the sigma mass, as defined in the random phase approximation, does not vanish. We also compute the adiabatic lines in the (T, µ B ) plane. Within the models studied here, the critical point does not serve as a "focusing" point in the adiabatic expansion.

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Thermodynamical properties of nuclear matter undergoing multifragmentation are studied within a simplified version of the statistical model. An exact analytical solution has been found for the grand canonical ensemble. Excluded volume effects are taken into account in the thermodynamically self-consistent way. In thermodynamic limit the model exhibits a first order liquid-gas phase transition with specific mixed phase properties. An extension of the model including the Fisher's term is also studied. The possibility of the second order phase transition at or above the critical point is demonstrated. The fragment mass distributions in the different regions of the phase diagram are discussed.

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Compact stars consisting of fermions with arbitrary masses and interaction strengths are studied by solving the structure equation of general relativity, the Tolman-Oppenheimer-Volkoff equations. Scaling solutions are derived for a free and an interacting Fermi gas and tested by numerical calculations. We demonstrate that there is a unique mass-radius relation for compact stars made of free fermions which is independent of the fermion mass. For sufficiently strong interactions, the maximum stable mass of compact stars and its radius are controlled by the parameter of the interaction, both increasing linearly with the interaction strength. The mass-radius relation for compact stars made of strongly interacting fermions shows that the radius remains approximately constant for a wide range of compact star masses.Comment: 19 pages, 8 figures, refs. added, version to appear in Physical Review